71.9.14 problem 16

Internal problem ID [14493]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 06:42:28 AM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y^{\prime \prime }-4 y&=31 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-9\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 18

dsolve([diff(y(x),x$2)-4*y(x)=31,y(0) = -9, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = \frac {7 \,{\mathrm e}^{2 x}}{8}-\frac {17 \,{\mathrm e}^{-2 x}}{8}-\frac {31}{4} \]

✓ Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 25

DSolve[{D[y[x],{x,2}]-4*y[x]==31,{y[0]==-9,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} \left (-17 e^{-2 x}+7 e^{2 x}-62\right ) \]